The 3D higher order organization of chromatin within the nucleus of eukaryotic cells has so far remained elusive. A wealth of relevant information, however, is increasingly becoming available from chromosome conformation capture (3C) and related experimental techniques, which measure the probabilities of contact between large numbers of genomic sites in fixed cells. Such contact probabilities (CPs) can in principle be used to deduce the 3D spatial organization of chromatin. Here, we propose a computational method to recover an ensemble of chromatin conformations consistent with a set of given CPs. Compared with existing alternatives, this method does not require conversion of CPs to mean spatial distances. Instead, we estimate CPs by simulating a physically realistic, bead-chain polymer model of the 30-nm chromatin fiber. We then use an approach from adaptive filter theory to iteratively adjust the parameters of this polymer model until the estimated CPs match the given CPs. We have validated this method against reference data sets obtained from simulations of test systems with up to 45 beads and 4 loops. With additional testing against experiments and with further algorithmic refinements, our approach could become a valuable tool for researchers examining the higher order organization of chromatin.